Solve 280x^61-500-1000-1400-1500-20001000

Question

Simplify the expression

280 x^{6} - 20005400

Evaluate

280 x^{6} \times 1 - 500 - 1000 - 1400 - 1500 - 20001000

Multiply the terms

280 x^{6} - 500 - 1000 - 1400 - 1500 - 20001000

Solution

280 x^{6} - 20005400

Show Solution

40 (7 x^{6} - 500135)

Evaluate

280 x^{6} \times 1 - 500 - 1000 - 1400 - 1500 - 20001000

Multiply the terms

280 x^{6} - 500 - 1000 - 1400 - 1500 - 20001000

Subtract the numbers

280 x^{6} - 1500 - 1400 - 1500 - 20001000

Subtract the numbers

280 x^{6} - 2900 - 1500 - 20001000

Subtract the numbers

280 x^{6} - 4400 - 20001000

Subtract the numbers

280 x^{6} - 20005400

Solution

40 (7 x^{6} - 500135)

Show Solution

x_{1} = - \frac{6 8405768945}{7}, x_{2} = \frac{6 8405768945}{7}

Alternative Form

x_{1} \approx - 6.441666, x_{2} \approx 6.441666

Evaluate

280 x^{6} \times 1 - 500 - 1000 - 1400 - 1500 - 20001000

To find the roots of the expression,set the expression equal to 0

280 x^{6} \times 1 - 500 - 1000 - 1400 - 1500 - 20001000 = 0

Multiply the terms

280 x^{6} - 500 - 1000 - 1400 - 1500 - 20001000 = 0

Subtract the numbers

280 x^{6} - 1500 - 1400 - 1500 - 20001000 = 0

Subtract the numbers

280 x^{6} - 2900 - 1500 - 20001000 = 0

Subtract the numbers

280 x^{6} - 4400 - 20001000 = 0

Subtract the numbers

280 x^{6} - 20005400 = 0

Move the constant to the right-hand side and change its sign

280 x^{6} = 0 + 20005400

Removing 0 doesn't change the value,so remove it from the expression

280 x^{6} = 20005400

Divide both sides

\frac{280 x ^{6}}{280} = \frac{20005400}{280}

Divide the numbers

x^{6} = \frac{20005400}{280}

Cancel out the common factor 40

x^{6} = \frac{500135}{7}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 6 \frac{500135}{7}

Simplify the expression

More Steps

Evaluate

6 \frac{500135}{7}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{6 500135}{6 7}

Multiply by the Conjugate

\frac{6 500135 \times 6 7 ^{5}}{6 7 \times 6 7 ^{5}}

Simplify

\frac{6 500135 \times 6 16807}{6 7 \times 6 7 ^{5}}

Multiply the numbers

More Steps

Evaluate

6500135 \times 616807

The product of roots with the same index is equal to the root of the product

6 500135 \times 16807

Calculate the product

68405768945

\frac{6 8405768945}{6 7 \times 6 7 ^{5}}

Multiply the numbers

More Steps

Evaluate

67 \times 6 7^{5}

The product of roots with the same index is equal to the root of the product

6 7 \times 7^{5}

Calculate the product

6 7^{6}

Reduce the index of the radical and exponent with 6

7

\frac{6 8405768945}{7}

x = \pm \frac{6 8405768945}{7}

Separate the equation into 2 possible cases

x = \frac{6 8405768945}{7} x = - \frac{6 8405768945}{7}

Solution

x_{1} = - \frac{6 8405768945}{7}, x_{2} = \frac{6 8405768945}{7}

Alternative Form

x_{1} \approx - 6.441666, x_{2} \approx 6.441666

Show Solution